Simplify the expression. $(3k^{3}-6k^{2})(-4k^{3}+4k^{2}-2k)$
First use the distributive property. $ 3 k^3 (-4 k^3) + 3 k^3 (4 k^2) + 3 k^3 (-2 k) - 6 k^2 (-4 k^3) - 6 k^2 (4 k^2) - 6 k^2 (-2 k) $ Simplify. $ - 12k^{6} + 12k^{5} - 6k^{4} + 24k^{5} - 24k^{4} + 12k^{3} $ $-12k^{6}+36k^{5}-30k^{4}+12k^{3}$ Identify like terms. $ {- 12k^{6}} \color{#DF0030} {+ 12k^{5}} {- 6k^{4}} \color{#DF0030} {+ 24k^{5}} {- 24k^{4}} {+ 12k^{3}} $ Add the coefficients. $ { -12k^{6}} \color{#DF0030} {+ 36k^{5}} { -30k^{4}} {+ 12k^{3}} $